%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU890^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:02:36 PM UTC 2025 % Result : Theorem 7.02s 7.20s % Output : Proof 7.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU890^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 06:00:38 EDT 2025 % 0.13/0.34 % CPUTime : % 7.02/7.20 SZS status Theorem for theBenchmark.p % 7.02/7.20 SZS output start Proof for theBenchmark.p % 7.02/7.20 Clause #0 (by assumption #[]): Eq % 7.02/7.20 (Not % 7.02/7.20 (∀ (Xx : a), % 7.02/7.20 Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq Xx (cF Xt))) % 7.02/7.20 (Exists fun Xt => And (cS Xt) (Eq Xx (cF (cG Xt)))))) % 7.02/7.20 True % 7.02/7.20 Clause #1 (by clausification #[0]): Eq % 7.02/7.20 (∀ (Xx : a), % 7.02/7.20 Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq Xx (cF Xt))) % 7.02/7.20 (Exists fun Xt => And (cS Xt) (Eq Xx (cF (cG Xt))))) % 7.02/7.20 False % 7.02/7.20 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 7.02/7.20 Eq % 7.02/7.20 (Not % 7.02/7.20 (Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) % 7.02/7.20 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))))) % 7.02/7.20 True % 7.02/7.20 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 7.02/7.20 Eq % 7.02/7.20 (Iff (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) % 7.02/7.20 (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt))))) % 7.02/7.20 False % 7.02/7.20 Clause #4 (by clausification #[3]): ∀ (a_1 : a), % 7.02/7.20 Or (Eq (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) False) % 7.02/7.20 (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) False) % 7.02/7.20 Clause #5 (by clausification #[3]): ∀ (a_1 : a), % 7.02/7.20 Or (Eq (Exists fun Xt => And (Exists fun Xt0 => And (cS Xt0) (Eq Xt (cG Xt0))) (Eq (skS.0 0 a_1) (cF Xt))) True) % 7.02/7.20 (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) True) % 7.02/7.20 Clause #6 (by clausification #[4]): ∀ (a_1 : a) (a_2 : b), % 7.02/7.20 Or (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) False) % 7.02/7.20 (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq a_2 (cG Xt0))) (Eq (skS.0 0 a_1) (cF a_2))) False) % 7.02/7.20 Clause #7 (by clausification #[6]): ∀ (a_1 : b) (a_2 : a) (a_3 : c), % 7.02/7.20 Or (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq a_1 (cG Xt0))) (Eq (skS.0 0 a_2) (cF a_1))) False) % 7.02/7.20 (Eq (And (cS a_3) (Eq (skS.0 0 a_2) (cF (cG a_3)))) False) % 7.02/7.20 Clause #8 (by clausification #[7]): ∀ (a_1 : c) (a_2 : a) (a_3 : b), % 7.02/7.20 Or (Eq (And (cS a_1) (Eq (skS.0 0 a_2) (cF (cG a_1)))) False) % 7.02/7.20 (Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq a_3 (cG Xt0))) False) (Eq (Eq (skS.0 0 a_2) (cF a_3)) False)) % 7.02/7.20 Clause #9 (by clausification #[8]): ∀ (a_1 : b) (a_2 : a) (a_3 : c), % 7.02/7.20 Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq a_1 (cG Xt0))) False) % 7.02/7.20 (Or (Eq (Eq (skS.0 0 a_2) (cF a_1)) False) (Or (Eq (cS a_3) False) (Eq (Eq (skS.0 0 a_2) (cF (cG a_3))) False))) % 7.02/7.20 Clause #10 (by clausification #[9]): ∀ (a_1 : a) (a_2 : b) (a_3 a_4 : c), % 7.02/7.20 Or (Eq (Eq (skS.0 0 a_1) (cF a_2)) False) % 7.02/7.20 (Or (Eq (cS a_3) False) % 7.02/7.20 (Or (Eq (Eq (skS.0 0 a_1) (cF (cG a_3))) False) (Eq (And (cS a_4) (Eq a_2 (cG a_4))) False))) % 7.02/7.20 Clause #11 (by clausification #[10]): ∀ (a_1 : c) (a_2 : a) (a_3 : c) (a_4 : b), % 7.02/7.20 Or (Eq (cS a_1) False) % 7.02/7.20 (Or (Eq (Eq (skS.0 0 a_2) (cF (cG a_1))) False) % 7.02/7.20 (Or (Eq (And (cS a_3) (Eq a_4 (cG a_3))) False) (Ne (skS.0 0 a_2) (cF a_4)))) % 7.02/7.20 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : c) (a_3 : b) (a_4 : a), % 7.02/7.20 Or (Eq (cS a_1) False) % 7.02/7.20 (Or (Eq (And (cS a_2) (Eq a_3 (cG a_2))) False) (Or (Ne (skS.0 0 a_4) (cF a_3)) (Ne (skS.0 0 a_4) (cF (cG a_1))))) % 7.02/7.20 Clause #13 (by clausification #[12]): ∀ (a_1 : c) (a_2 : a) (a_3 : b) (a_4 : c), % 7.02/7.20 Or (Eq (cS a_1) False) % 7.02/7.20 (Or (Ne (skS.0 0 a_2) (cF a_3)) % 7.02/7.20 (Or (Ne (skS.0 0 a_2) (cF (cG a_1))) (Or (Eq (cS a_4) False) (Eq (Eq a_3 (cG a_4)) False)))) % 7.02/7.20 Clause #14 (by clausification #[13]): ∀ (a_1 : c) (a_2 : a) (a_3 : b) (a_4 : c), % 7.02/7.20 Or (Eq (cS a_1) False) % 7.02/7.20 (Or (Ne (skS.0 0 a_2) (cF a_3)) (Or (Ne (skS.0 0 a_2) (cF (cG a_1))) (Or (Eq (cS a_4) False) (Ne a_3 (cG a_4))))) % 7.02/7.20 Clause #15 (by destructive equality resolution #[14]): ∀ (a_1 : c) (a_2 : a) (a_3 : c), % 7.02/7.20 Or (Eq (cS a_1) False) (Or (Ne (skS.0 0 a_2) (cF (cG a_3))) (Or (Ne (skS.0 0 a_2) (cF (cG a_1))) (Eq (cS a_3) False))) % 7.02/7.20 Clause #16 (by clausification #[5]): ∀ (a_1 : a) (a_2 : b), % 7.02/7.20 Or (Eq (Exists fun Xt => And (cS Xt) (Eq (skS.0 0 a_1) (cF (cG Xt)))) True) % 7.02/7.20 (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))) % 7.07/7.23 True) % 7.07/7.23 Clause #17 (by clausification #[16]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 7.07/7.23 Or % 7.07/7.23 (Eq (And (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)))) % 7.07/7.23 True) % 7.07/7.23 (Eq (And (cS (skS.0 2 a_1 a_3)) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3))))) True) % 7.07/7.23 Clause #18 (by clausification #[17]): ∀ (a_1 : a) (a_2 : c) (a_3 : b), % 7.07/7.23 Or (Eq (And (cS (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2))))) True) % 7.07/7.23 (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) True) % 7.07/7.23 Clause #19 (by clausification #[17]): ∀ (a_1 : a) (a_2 : c) (a_3 : b), % 7.07/7.23 Or (Eq (And (cS (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2))))) True) % 7.07/7.23 (Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_3) (cG Xt0))) True) % 7.07/7.23 Clause #20 (by clausification #[18]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 7.07/7.23 Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True) (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3)))) True) % 7.07/7.23 Clause #21 (by clausification #[18]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Eq (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) True) (Eq (cS (skS.0 2 a_1 a_3)) True) % 7.07/7.23 Clause #22 (by clausification #[20]): ∀ (a_1 : a) (a_2 : c) (a_3 : b), % 7.07/7.23 Or (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.07/7.23 Clause #23 (by clausification #[22]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3)))) % 7.07/7.23 Clause #24 (by clausification #[21]): ∀ (a_1 : a) (a_2 : c) (a_3 : b), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.07/7.23 Clause #25 (by superposition #[24, 15]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 a_5 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.07/7.23 (Or (Eq True False) % 7.07/7.23 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 2 a_1 a_5)))) (Eq (cS a_4) False)))) % 7.07/7.23 Clause #26 (by clausification #[25]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 a_5 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.07/7.23 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 2 a_1 a_5)))) (Eq (cS a_4) False))) % 7.07/7.23 Clause #27 (by superposition #[26, 23]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b) (a_5 : a) (a_6 a_7 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.07/7.23 (Or (Eq (skS.0 0 a_3) (cF (skS.0 1 a_3 a_4))) % 7.07/7.23 (Or (Ne (skS.0 0 a_5) (skS.0 0 a_1)) % 7.07/7.23 (Or (Ne (skS.0 0 a_5) (cF (cG (skS.0 2 a_3 a_6)))) (Eq (cS (skS.0 2 a_1 a_7)) False)))) % 7.07/7.23 Clause #28 (by clausification #[19]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 7.07/7.23 Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) True) % 7.07/7.23 (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_3)))) True) % 7.07/7.23 Clause #29 (by clausification #[19]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 7.07/7.23 Or (Eq (Exists fun Xt0 => And (cS Xt0) (Eq (skS.0 1 a_1 a_2) (cG Xt0))) True) (Eq (cS (skS.0 2 a_1 a_3)) True) % 7.07/7.23 Clause #30 (by clausification #[28]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.07/7.23 Or (Eq (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) True) % 7.07/7.23 (Eq (And (cS (skS.0 3 a_1 a_3 a_4)) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 3 a_1 a_3 a_4)))) True) % 7.07/7.23 Clause #31 (by clausification #[30]): ∀ (a_1 : a) (a_2 : b) (a_3 a_4 : c), % 7.07/7.23 Or (Eq (And (cS (skS.0 3 a_1 a_2 a_3)) (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)))) True) % 7.07/7.23 (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_4)))) % 7.07/7.23 Clause #32 (by clausification #[31]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) (Eq (Eq (skS.0 1 a_1 a_3) (cG (skS.0 3 a_1 a_3 a_4))) True) % 7.07/7.23 Clause #33 (by clausification #[31]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) (Eq (cS (skS.0 3 a_1 a_3 a_4)) True) % 7.07/7.23 Clause #34 (by clausification #[32]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (cG (skS.0 2 a_1 a_2)))) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 3 a_1 a_3 a_4))) % 7.07/7.23 Clause #37 (by equality resolution #[27]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 : b) (a_5 a_6 : c), % 7.07/7.23 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_3) (cF (skS.0 1 a_3 a_4))) % 7.09/7.26 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_3 a_5)))) (Eq (cS (skS.0 2 a_1 a_6)) False))) % 7.09/7.26 Clause #40 (by clausification #[29]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.09/7.26 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.26 (Eq (And (cS (skS.0 4 a_1 a_3 a_4)) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 4 a_1 a_3 a_4)))) True) % 7.09/7.26 Clause #41 (by clausification #[40]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.09/7.26 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (Eq (skS.0 1 a_1 a_3) (cG (skS.0 4 a_1 a_3 a_4))) True) % 7.09/7.26 Clause #42 (by clausification #[40]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (cS (skS.0 4 a_1 a_3 a_4)) True) % 7.09/7.26 Clause #43 (by clausification #[41]): ∀ (a_1 : a) (a_2 : c) (a_3 : b) (a_4 : c), % 7.09/7.26 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (skS.0 1 a_1 a_3) (cG (skS.0 4 a_1 a_3 a_4))) % 7.09/7.26 Clause #47 (by superposition #[42, 15]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : b) (a_6 : c), % 7.09/7.26 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.26 (Or (Eq True False) % 7.09/7.26 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 4 a_1 a_5 a_6)))) (Eq (cS a_4) False)))) % 7.09/7.26 Clause #54 (by clausification #[47]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : b) (a_6 : c), % 7.09/7.26 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.26 (Or (Ne (skS.0 0 a_3) (cF (cG a_4))) (Or (Ne (skS.0 0 a_3) (cF (cG (skS.0 4 a_1 a_5 a_6)))) (Eq (cS a_4) False))) % 7.09/7.26 Clause #59 (by superposition #[54, 43]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : a) (a_6 a_7 : b) (a_8 a_9 : c), % 7.09/7.26 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.26 (Or (Eq (cS (skS.0 2 a_3 a_4)) True) % 7.09/7.26 (Or (Ne (skS.0 0 a_5) (cF (skS.0 1 a_1 a_6))) % 7.09/7.26 (Or (Ne (skS.0 0 a_5) (cF (cG (skS.0 4 a_3 a_7 a_8)))) (Eq (cS (skS.0 4 a_1 a_6 a_9)) False)))) % 7.09/7.26 Clause #73 (by superposition #[37, 23]): ∀ (a_1 : a) (a_2 : b) (a_3 : a) (a_4 a_5 : b) (a_6 : c), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_3) (cF (skS.0 1 a_3 a_4))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_5))) % 7.09/7.26 (Or (Ne (skS.0 0 a_3) (skS.0 0 a_1)) (Eq (cS (skS.0 2 a_3 a_6)) False)))) % 7.09/7.26 Clause #308 (by equality resolution #[73]): ∀ (a_1 : a) (a_2 a_3 a_4 : b) (a_5 : c), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))) (Eq (cS (skS.0 2 a_1 a_5)) False))) % 7.09/7.26 Clause #309 (by superposition #[308, 24]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : b), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))) (Or (Eq False True) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_5)))))) % 7.09/7.26 Clause #314 (by clausification #[309]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : b), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_5))))) % 7.09/7.26 Clause #328 (by equality factoring #[314]): ∀ (a_1 : a) (a_2 a_3 a_4 : b), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.09/7.26 (Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4))))) % 7.09/7.26 Clause #329 (by eliminate resolved literals #[328]): ∀ (a_1 : a) (a_2 a_3 a_4 : b), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_4)))) % 7.09/7.26 Clause #343 (by equality factoring #[329]): ∀ (a_1 : a) (a_2 a_3 : b), % 7.09/7.26 Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 (Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3)))) % 7.09/7.26 Clause #344 (by eliminate resolved literals #[343]): ∀ (a_1 : a) (a_2 a_3 : b), Or (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_3))) % 7.09/7.26 Clause #358 (by equality factoring #[344]): ∀ (a_1 : a) (a_2 : b), Or (Ne (skS.0 0 a_1) (skS.0 0 a_1)) (Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2))) % 7.09/7.26 Clause #359 (by eliminate resolved literals #[358]): ∀ (a_1 : a) (a_2 : b), Eq (skS.0 0 a_1) (cF (skS.0 1 a_1 a_2)) % 7.09/7.26 Clause #369 (by backward demodulation #[359, 59]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : a) (a_6 : b) (a_7 : c) (a_8 : b) (a_9 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_3 a_4)) True) % 7.09/7.29 (Or (Ne (skS.0 0 a_5) (skS.0 0 a_1)) % 7.09/7.29 (Or (Ne (skS.0 0 a_5) (cF (cG (skS.0 4 a_3 a_6 a_7)))) (Eq (cS (skS.0 4 a_1 a_8 a_9)) False)))) % 7.09/7.29 Clause #402 (by equality resolution #[369]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c) (a_5 : b) (a_6 : c) (a_7 : b) (a_8 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_3 a_4)) True) % 7.09/7.29 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 4 a_3 a_5 a_6)))) (Eq (cS (skS.0 4 a_1 a_7 a_8)) False))) % 7.09/7.29 Clause #403 (by superposition #[402, 43]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 a_5 : c) (a_6 a_7 : b) (a_8 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_3 a_4)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_5)) True) % 7.09/7.29 (Or (Ne (skS.0 0 a_3) (cF (skS.0 1 a_1 a_6))) (Eq (cS (skS.0 4 a_3 a_7 a_8)) False)))) % 7.09/7.29 Clause #404 (by forward demodulation #[403, 359]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 a_5 : c) (a_6 : b) (a_7 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_3 a_4)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_5)) True) (Or (Ne (skS.0 0 a_3) (skS.0 0 a_1)) (Eq (cS (skS.0 4 a_3 a_6 a_7)) False)))) % 7.09/7.29 Clause #405 (by equality resolution #[404]): ∀ (a_1 : a) (a_2 a_3 a_4 : c) (a_5 : b) (a_6 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Eq (cS (skS.0 4 a_1 a_5 a_6)) False))) % 7.09/7.29 Clause #406 (by superposition #[405, 42]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Or (Eq (cS (skS.0 2 a_1 a_5)) True) (Eq False True)))) % 7.09/7.29 Clause #408 (by clausification #[406]): ∀ (a_1 : a) (a_2 a_3 a_4 a_5 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Eq (cS (skS.0 2 a_1 a_5)) True))) % 7.09/7.29 Clause #413 (by equality factoring #[408]): ∀ (a_1 : a) (a_2 a_3 a_4 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Ne True True) (Eq (cS (skS.0 2 a_1 a_4)) True))) % 7.09/7.29 Clause #414 (by clausification #[413]): ∀ (a_1 : a) (a_2 a_3 a_4 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Or (Eq True False) (Eq True False)))) % 7.09/7.29 Clause #416 (by clausification #[414]): ∀ (a_1 : a) (a_2 a_3 a_4 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq (cS (skS.0 2 a_1 a_4)) True) (Eq True False))) % 7.09/7.29 Clause #417 (by clausification #[416]): ∀ (a_1 : a) (a_2 a_3 a_4 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Eq (cS (skS.0 2 a_1 a_4)) True)) % 7.09/7.29 Clause #422 (by equality factoring #[417]): ∀ (a_1 : a) (a_2 a_3 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Ne True True) (Eq (cS (skS.0 2 a_1 a_3)) True)) % 7.09/7.29 Clause #423 (by clausification #[422]): ∀ (a_1 : a) (a_2 a_3 : c), % 7.09/7.29 Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Or (Eq True False) (Eq True False))) % 7.09/7.29 Clause #425 (by clausification #[423]): ∀ (a_1 : a) (a_2 a_3 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq (cS (skS.0 2 a_1 a_3)) True) (Eq True False)) % 7.09/7.29 Clause #426 (by clausification #[425]): ∀ (a_1 : a) (a_2 a_3 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq (cS (skS.0 2 a_1 a_3)) True) % 7.09/7.29 Clause #429 (by equality factoring #[426]): ∀ (a_1 : a) (a_2 : c), Or (Ne True True) (Eq (cS (skS.0 2 a_1 a_2)) True) % 7.09/7.29 Clause #430 (by clausification #[429]): ∀ (a_1 : a) (a_2 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Eq True False)) % 7.09/7.29 Clause #432 (by clausification #[430]): ∀ (a_1 : a) (a_2 : c), Or (Eq (cS (skS.0 2 a_1 a_2)) True) (Eq True False) % 7.09/7.29 Clause #433 (by clausification #[432]): ∀ (a_1 : a) (a_2 : c), Eq (cS (skS.0 2 a_1 a_2)) True % 7.09/7.29 Clause #434 (by superposition #[433, 15]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c), % 7.09/7.29 Or (Eq True False) % 7.16/7.31 (Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_3 a_4)))) (Eq (cS a_2) False))) % 7.16/7.31 Clause #435 (by clausification #[434]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : c), % 7.16/7.31 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_3 a_4)))) (Eq (cS a_2) False)) % 7.16/7.31 Clause #436 (by superposition #[435, 34]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 a_5 : a) (a_6 a_7 : c), % 7.16/7.31 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) % 7.16/7.31 (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1)) % 7.16/7.31 (Or (Ne (skS.0 0 a_4) (cF (cG (skS.0 2 a_5 a_6)))) (Eq (cS (skS.0 2 a_1 a_7)) False))) % 7.16/7.31 Clause #437 (by superposition #[435, 33]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 a_5 : a) (a_6 a_7 : c), % 7.16/7.31 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) % 7.16/7.31 (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1)) % 7.16/7.31 (Or (Ne (skS.0 0 a_4) (cF (cG (skS.0 2 a_5 a_6)))) (Eq (cS (skS.0 2 a_1 a_7)) False))) % 7.16/7.31 Clause #443 (by equality resolution #[437]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 a_6 : c), % 7.16/7.31 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) % 7.16/7.31 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_4 a_5)))) (Eq (cS (skS.0 2 a_1 a_6)) False)) % 7.16/7.31 Clause #445 (by superposition #[443, 33]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 : b) (a_6 a_7 : c), % 7.16/7.31 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) % 7.16/7.31 (Or (Eq (cS (skS.0 3 a_4 a_5 a_6)) True) (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1)) (Eq (cS (skS.0 2 a_4 a_7)) False))) % 7.16/7.31 Clause #446 (by equality resolution #[445]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 a_6 : c), % 7.16/7.31 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Or (Eq (cS (skS.0 3 a_1 a_4 a_5)) True) (Eq (cS (skS.0 2 a_1 a_6)) False)) % 7.16/7.31 Clause #447 (by superposition #[446, 433]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c), % 7.16/7.31 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Or (Eq (cS (skS.0 3 a_1 a_4 a_5)) True) (Eq False True)) % 7.16/7.31 Clause #448 (by clausification #[447]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c), % 7.16/7.31 Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Eq (cS (skS.0 3 a_1 a_4 a_5)) True) % 7.16/7.31 Clause #450 (by equality factoring #[448]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Ne True True) (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) % 7.16/7.31 Clause #451 (by clausification #[450]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Or (Eq True False) (Eq True False)) % 7.16/7.31 Clause #453 (by clausification #[451]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Or (Eq (cS (skS.0 3 a_1 a_2 a_3)) True) (Eq True False) % 7.16/7.31 Clause #454 (by clausification #[453]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (cS (skS.0 3 a_1 a_2 a_3)) True % 7.16/7.31 Clause #455 (by superposition #[454, 15]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : b) (a_5 : c), % 7.16/7.31 Or (Eq True False) % 7.16/7.31 (Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 3 a_3 a_4 a_5)))) (Eq (cS a_2) False))) % 7.16/7.31 Clause #456 (by clausification #[455]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : b) (a_5 : c), % 7.16/7.31 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 3 a_3 a_4 a_5)))) (Eq (cS a_2) False)) % 7.16/7.31 Clause #462 (by equality resolution #[436]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 a_6 : c), % 7.16/7.31 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) % 7.16/7.31 (Or (Ne (skS.0 0 a_1) (cF (cG (skS.0 2 a_4 a_5)))) (Eq (cS (skS.0 2 a_1 a_6)) False)) % 7.16/7.31 Clause #463 (by superposition #[462, 34]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : a) (a_5 : b) (a_6 a_7 : c), % 7.16/7.31 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) % 7.16/7.31 (Or (Eq (skS.0 1 a_4 a_5) (cG (skS.0 3 a_4 a_5 a_6))) % 7.16/7.31 (Or (Ne (skS.0 0 a_4) (skS.0 0 a_1)) (Eq (cS (skS.0 2 a_4 a_7)) False))) % 7.16/7.31 Clause #473 (by equality resolution #[463]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 a_6 : c), % 7.16/7.31 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) % 7.16/7.31 (Or (Eq (skS.0 1 a_1 a_4) (cG (skS.0 3 a_1 a_4 a_5))) (Eq (cS (skS.0 2 a_1 a_6)) False)) % 7.16/7.31 Clause #474 (by superposition #[473, 433]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c), % 7.16/7.31 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) % 7.16/7.31 (Or (Eq (skS.0 1 a_1 a_4) (cG (skS.0 3 a_1 a_4 a_5))) (Eq False True)) % 7.16/7.31 Clause #475 (by clausification #[474]): ∀ (a_1 : a) (a_2 : b) (a_3 : c) (a_4 : b) (a_5 : c), % 7.16/7.33 Or (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) (Eq (skS.0 1 a_1 a_4) (cG (skS.0 3 a_1 a_4 a_5))) % 7.16/7.33 Clause #479 (by equality factoring #[475]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), % 7.16/7.33 Or (Ne (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3))) % 7.16/7.33 Clause #480 (by eliminate resolved literals #[479]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (skS.0 1 a_1 a_2) (cG (skS.0 3 a_1 a_2 a_3)) % 7.16/7.33 Clause #481 (by backward demodulation #[480, 456]): ∀ (a_1 : a) (a_2 : c) (a_3 : a) (a_4 : b), % 7.16/7.33 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (cF (skS.0 1 a_3 a_4))) (Eq (cS a_2) False)) % 7.16/7.33 Clause #485 (by forward demodulation #[481, 359]): ∀ (a_1 : a) (a_2 : c) (a_3 : a), % 7.16/7.33 Or (Ne (skS.0 0 a_1) (cF (cG a_2))) (Or (Ne (skS.0 0 a_1) (skS.0 0 a_3)) (Eq (cS a_2) False)) % 7.16/7.33 Clause #486 (by superposition #[485, 480]): ∀ (a_1 a_2 : a) (a_3 : b) (a_4 : a) (a_5 : c), % 7.16/7.33 Or (Ne (skS.0 0 a_1) (cF (skS.0 1 a_2 a_3))) % 7.16/7.33 (Or (Ne (skS.0 0 a_1) (skS.0 0 a_4)) (Eq (cS (skS.0 3 a_2 a_3 a_5)) False)) % 7.16/7.33 Clause #487 (by forward demodulation #[486, 359]): ∀ (a_1 a_2 a_3 : a) (a_4 : b) (a_5 : c), % 7.16/7.33 Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Or (Ne (skS.0 0 a_1) (skS.0 0 a_3)) (Eq (cS (skS.0 3 a_2 a_4 a_5)) False)) % 7.16/7.33 Clause #488 (by equality resolution #[487]): ∀ (a_1 a_2 : a) (a_3 : b) (a_4 : c), Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Eq (cS (skS.0 3 a_1 a_3 a_4)) False) % 7.16/7.33 Clause #489 (by equality resolution #[488]): ∀ (a_1 : a) (a_2 : b) (a_3 : c), Eq (cS (skS.0 3 a_1 a_2 a_3)) False % 7.16/7.33 Clause #490 (by superposition #[489, 454]): Eq False True % 7.16/7.33 Clause #491 (by clausification #[490]): False % 7.16/7.33 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------